Secure Distributed Matrix Multiplication with Precomputation
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arXiv
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| Main Authors: | , , , , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866910441739911168 |
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| author | Cartor, Ryann D'Oliveira, Rafael G. L. Rouayheb, Salim El Heinlein, Daniel Karpuk, David Sprintson, Alex |
| author_facet | Cartor, Ryann D'Oliveira, Rafael G. L. Rouayheb, Salim El Heinlein, Daniel Karpuk, David Sprintson, Alex |
| contents | We consider the problem of secure distributed matrix multiplication in which a user wishes to compute the product of two matrices with the assistance of honest but curious servers. We show how to construct polynomial schemes for the outer product partitioning which take advantage of the user's ability to precompute, and provide bounds for our technique. We show that precomputation allows for a reduction in the order of the time complexity for the cases where the number of colluding servers is a fixed percentage of the number of servers. Furthermore, with precomputation, any percentage (less than 100%) of collusions can be tolerated, compared to the upper limit of 50% for the case without precomputation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_06121 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Secure Distributed Matrix Multiplication with Precomputation Cartor, Ryann D'Oliveira, Rafael G. L. Rouayheb, Salim El Heinlein, Daniel Karpuk, David Sprintson, Alex Information Theory We consider the problem of secure distributed matrix multiplication in which a user wishes to compute the product of two matrices with the assistance of honest but curious servers. We show how to construct polynomial schemes for the outer product partitioning which take advantage of the user's ability to precompute, and provide bounds for our technique. We show that precomputation allows for a reduction in the order of the time complexity for the cases where the number of colluding servers is a fixed percentage of the number of servers. Furthermore, with precomputation, any percentage (less than 100%) of collusions can be tolerated, compared to the upper limit of 50% for the case without precomputation. |
| title | Secure Distributed Matrix Multiplication with Precomputation |
| topic | Information Theory |
| url | https://arxiv.org/abs/2405.06121 |